Negotiators will be meeting daily in advance of another summit next month

Netanyahu and Abbas met alone at State Department on Thursday

Washington (CNN) -- After two days of meetings and talks led by President Barack Obama and Secretary of State Hillary Clinton, Israeli and Palestinian leaders leave Washington deadlocked over the contentious issue of Israeli settlements.

Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas met alone behind closed doors for more than an hour and a half Thursday in a State Department room just outside Clinton's office. The one-on-one meeting followed their on-camera pledges to move the peace process forward and their hardy handshake with Clinton in the middle.

But several diplomatic sources involved in the summit said the two leaders emerged from their meeting in a stalemate over whether Israeli settlements should continue.

The two leaders met with Clinton to give a readout of their meeting.

According to Fadi Elsalameen, who accompanied Abbas, the two leaders were very blunt about their opposing views.

Netanyahu is under pressure from the Palestinians and the Obama administration to extend a 10-month moratorium on building Israeli settlements in the disputed West Bank territory. That moratorium is set to expire September 26. Netanyahu's conservative coalition government wants the Israeli prime minister to end the moratorium.

Elsalameen said that during the leaders' private discussion, Abbas asked Netanyahu to extend the settlement freeze.

Netanyahu reportedly said, "I cannot extend."

Elsalameen says Abbas responded, "Then I cannot continue."

Before the summit even began, Abbas had threatened to abandon final status talks if Netanyahu allowed Israeli settlements to go forward. The Palestinian leader is trying to show he'll keep his word.

Elsalameen said Clinton was asked about what would happen if Israel continued to expand the controversial Jewish settlements. Elsalameen said Clinton responded, as Obama had publicly stated, "Then all bets are off."

Despite the standoff between the Palestinian and Israeli leadership, Elsalameen said that starting Sunday, their chief negotiators will meet on a daily basis to try to entertain compromises.

According to U.S., Israeli and Palestinian officials, the hope is that during those talks, some trust and confidence will be developed, and some of the other issues will be settled, possibly making it easier to find a formula for extending the moratorium.

The issue could then be discussed when Netanyahu and Abbas meet again in Egypt on September 14 and 15.

Both sides, and the Americans, fully expect some formula to be found at the last minute to extend the moratorium, the officials said. Obama told the leaders not to ruin this opportunity, according to the sources, and to make sure the 26th of September goes by quietly without incident

While nothing was agreed to, officials from both sides said the tone of this week's talks was fairly decent, and they expressed cautious optimism. Netanyahu was apparently in a good mood after the meetings, and Abbas, who was nervous and tense the night before the talks, seemed to come away from them in a better mood. He didn't feel pressured as he has been recently and was appearing to aides to be a little more relaxed and confident, they said.

Elsalameen said Abbas would be visiting Libya and Tunisia to drum up support for the Palestinian people.